Abstract
An approximate solution is obtained for the linearized system of Navier — Stokes equations at low Reynolds numbers with boundary conditions corresponding to the case when axisymmetric normal and radial tangential stresses act at the surface of a heavy, viscous incompressible fluid. The axisymmetric shape of the free surface is specified at the initial instant of time. An integral definition of its shape valid for considerable times is obtained for stationary perturbations at the surface. Existence of circular waves which not only propagate from the perturbation source but, also, towards it, is established. Examples are considered. Waves propagating from the perturbation source are also investigated. It is established that the main part of such waves is the same for low and high (see, e.g., [1 – 3]) Reynolds numbers.
Published Version
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